PAGE NO.:
A system of two electric dipoles, each of dipole moment
having magnitude p ade adšanged in the configudation
shown in figure. The electrostatic interaction energy of
this system of tao dipoles is.
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Answers
Answer:
Step-by-step explanation:
Electric dipoles on magnetic monopoles
in spin ice
D. I. Khomskii
II. Physikalisches Institut, Universit¨at zu K¨oln,
Z¨ulpicher Str. 77,
50937 K¨oln, Germany
Abstract
The close connection of electricity and magnetism is one of the cornerstones of modern physics. This connection plays crucial role from
the fundamental point of view and in practical applications, including
spintronics and multiferroic materials. A breakthrough was a recent
proposal that in magnetic materials called spin ice the elementary excitations have a magnetic charge and behave as magnetic monopoles. I
show that, besides magnetic charge, there should be an electric dipole
attached to each magnetic monopole. This opens new possibilities
to study and to control such monopoles by electric field. Thus the
electric–magnetic analogy goes even further than usually assumed:
whereas electrons have electric charge and magnetic dipole (spin),
magnetic monopoles in spin ice, while having magnetic charge, also
have electric dipole.
Introduction
Spin ice materials present a very interesting class of magnetic materials [1].
Mostly these are the pyrochlores with strongly anisotropic Ising-like rare
earth such as Dy or Ho [2], although they exist in other structures, and
one cannot exclude that similar materials could also be made on the basis
of transition metal elements with strong anisotropy, such as Co2+ or Fe2+.
Spin ice systems consist of a network of corner-shared metal tetrahedra with
1
effective ferromagnetic coupling between spins [3, 4], in which in the ground
state the Ising spins are ordered in two-in/two-out fashion. Artificial spin ice
systems with different structures have also been made [5, 6, 7, 8].
Spin ice systems are bona fide examples of frustrated systems, and they
attract now considerable attention, both because they are interesting in their
own right and because they can model different other systems, including real
water ice [9]. A new chapter in the study of spin ice was opened by the
suggestion that the natural elementary excitations in spin ice materials —
objects with 3-in/1-out or 1-in/3-out tetrahedra — have a magnetic charge
[10] and display many properties similar to those of magnetic monopoles [11].
Especially the last proposal gave rise to a flurry of activity, see e.g. [12], in
which, in particular, the close analogy between electric and magnetic phenomena was invoked. Thus, one can apply to their description many notions
developed for the description of systems of charges such as electrolytes; this
description proves to be very efficient for understanding many properties of
spin ice.
Until now the largest attention was paid to the magnetic properties of spin
ice, both static and dynamic, largely connected with monopole excitations
[13, 14, 15, 16, 17, 18], and the main tool to modify their properties was
magnetic field, which couples directly to spins or to the magnetic charge
of monopoles. I argue below that the magnetic monopoles in spin ice have
yet another characteristic which could allow for other ways to influence and
study them: each magnetic monopole, i.e. the tetrahedron with 3-in/1-out or
1-in/3-out configuration, shall also have an electric dipole localized at such
tetrahedron. This demonstrates once again the intrinsic interplay between
magnetic and electric properties of matter.
It is well known that some magnetic textures can break inversion symmetry – a necessary condition for creating electric dipoles. This lies at the heart
of magnetically-driven ferroelectricity in type-II multiferroics [19]. There exists, in particular, a purely electronic mechanism for creating electric dipoles.